HYBRID MACHINE LEARNING MODELING FOR EVALUATING HYDRAULIC FRACTURE CONDUCTIVITY USING STRAIN DATA FROM FIBER OPTICS

Description

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is the U.S. National Stage Application of the International Application No. PCT/US2023/068185, entitled “HYBRID MACHINE LEARNING MODELING FOR EVALUATING HYDRAULIC FRACTURE CONDUCTIVITY USING STRAIN DATA FROM FIBER OPTICS,” filed on Jun. 9, 2023, the disclosure of which is hereby incorporated by reference in its entirety, which claims the benefit of U.S. Provisional Application No. 63/366,416, filed Jun. 15, 2022, the disclosure of which is herein incorporated by reference in its entirety.

FIELD OF THE INVENTION

The techniques described herein relate generally to the field of hydrocarbon well completions and hydraulic fracturing operations. More specifically, the techniques described herein relate to hybrid machine learning modeling for evaluating hydraulic fracture conductivity using strain data from fiber optics.

BACKGROUND OF THE INVENTION

This section is intended to introduce various aspects of the art, which may be associated with embodiments of the present techniques. This discussion is believed to assist in providing a framework to facilitate a better understanding of particular aspects of the present techniques. Accordingly, it should be understood that this section should be read in this light, and not necessarily as admissions of prior art.

During the drilling and completion of a hydrocarbon well, a wellbore is drilled into a subterranean formation to promote the production of hydrocarbon fluids from a corresponding subterranean formation (or reservoir). In many cases, the subterranean formation needs to be stimulated in some manner to promote the production of the hydrocarbon fluids. Stimulation operations include any operation performed upon the matrix of a subterranean formation to improve hydraulic conductivity through such matrix. Hydraulic fracturing, in particular, is a common stimulation operation for unconventional reservoirs.

Hydraulic fracturing operations involve pumping large quantities of a pressurizing fluid stream (often referred to as “fracturing fluid”) into a subterranean formation under high hydraulic pressure to promote the formation of fractures within the matrix of the subterranean formation and to create high-conductivity flow paths. Moreover, as the pressurizing fluid stream is pumped into the formation, primary fractures extending from the wellbore and, in some instances, secondary fractures extending from the primary fractures, are formed. These fractures may be vertical, horizontal, or a combination of directions forming a tortuous path.

Once the pressurizing fluid stream has created the fractures within the subterranean formation, a proppant (e.g., typically consisting primarily of sand and/or ceramic beads) is pumped into the fractures to “prop” the fractures open after the hydraulic pressure has been released following the hydraulic fracturing operation. Specifically, upon reaching the fractures, the proppant settles within the fractures to form a proppant pack that prevents the fractures from closing once the hydraulic pressure has been released. In this manner, the proppant provides a long-term increase in fluid permeability within the near-wellbore region of the formation.

The success of the hydraulic fracturing process has a direct impact on the amount of hydrocarbon fluids that may be recovered from the reservoir. Specifically, the numbers, sizes, compliances, and locations of the fractures corresponding to the perforation clusters within each stage of the hydrocarbon well directly impact the amount of hydrocarbon fluids that are able to mobilize and flow into the wellbore. However, difficulties are often encountered during hydraulic fracturing operations, such as, in particular, difficulties associated with the deposition of proppant in fractures that have been created or extended under hydraulic pressure. In particular, effective transport of the proppant may be difficult due to settling, making it challenging to distribute the proppant into more remote reaches of a network of fractures. Therefore, it is desirable to obtain information regarding the manner in which the proppant transports through the fractures, particularly to far field. Such information can be used for well planning purposes, such as by enabling the estimation of optimal well spacing for the field. However, currently there is very limited understanding regarding how proppant transports through fractures. As a result, there is room for much improvement in this area.

SUMMARY OF THE INVENTION

An embodiment described herein provides a method for hydraulic fracturing conductivity evaluation with respect to a producer well. The method is executed via a processor of a computing system. The method includes measuring fracture-related data corresponding to a hydraulic fracturing operation performed with respect to one or more producer wells in a field, where the fracture-related data include strain data measured using one or more optical fibers deployed within one or more offset wells in the field. The method also includes extracting deep convolutional neural network (DCNN)-based features, physics-based features, and statistics-based features using the fracture-related data, as well as training a hybrid machine learning model for evaluating hydraulic fracture conductivity corresponding to the hydraulic fracturing operation, where the training is performed using the DCNN-based features, the physics-based features, and the statistics-based features. The method further includes applying the trained hybrid machine learning model to generate a well spacing plan for the field.

Another embodiment described herein provides a method for developing a field of producer wells. The method includes executing a hydraulic fracturing operation for a producer well in a field and generating fracture-related data corresponding to the hydraulic fracturing operation for the producer well using an offset well, where the fracture-related data include strain data measured using an optical fiber deployed within the offset well. The method also includes extracting DCNN-based features, physics-based features, and statistics-based features using the fracture-related data and training a hybrid machine learning model for evaluating hydraulic fracture conductivity corresponding to the hydraulic fracturing operation, where the training is performed using the DCNN-based features, the physics-based features, and the statistics-based features. The method further includes applying the trained hybrid machine learning model to generate a well spacing plan for the field and developing the field according to the generated well spacing plan.

Another embodiment described herein provides a computing system including a processor and a non-transitory, computer-readable storage medium. The non-transitory, computer-readable storage medium includes code configured to direct the processor to access fracture-related data corresponding to a hydraulic fracturing operation performed with respect to one or more producers well in a field, where the fracture-related data include strain data measured using one or more optical fibers deployed within one or more offset wells in the field. The non-transitory, computer-readable storage medium also includes code configured to direct the processor to extract DCNN-based features using the fracture-related data by performing deep-learning-based feature extraction, where performing the deep-learning-based feature extraction includes generating two-dimensional (2D) strain maps from the strain data, converting each 2D strain map to a strain rate map, averaging each strain rate map to a time series of averaged strain rate, calculating a Gramian Angular Field (GAF) map for each time series, loading each GAF map into a pretrained DCNN, removing top layers of the DCNN to generate an array of features, mapping the array of features to two or more principal components, and outputting the principal components as at least a portion of the DCNN-based features. The non-transitory, computer-readable storage medium also includes code configured to direct the processor to extract physics-based features using the fracture-related data by calculating at least a portion of the physics-based features from the 2D strain maps, as well as to extract statistics-based features using the fracture-related data. The non-transitory, computer-readable storage medium further includes code configured to direct the processor to train a hybrid machine learning model for evaluating hydraulic fracture conductivity corresponding to the hydraulic fracturing operation, where the training is performed using the pretrained DCNN, in combination with the DCNN-based features, the physics-based features, and the statistics-based features, as well as to apply the trained hybrid machine learning model to generate a well spacing plan for the field.

These and other features and attributes of the disclosed embodiments of the present techniques and their advantageous applications and/or uses will be apparent from the detailed description that follows.

BRIEF DESCRIPTION OF THE DRAWINGS

To assist those of ordinary skill in the relevant art in making and using the subject matter described herein, reference is made to the appended drawings, where:

FIG. 1 is a schematic view of an exemplary well that may be utilized in accordance with the present techniques;

FIG. 2 is a simplified schematic view of multiple wells that may be utilized in accordance with the present techniques, including a producer well and an offset well;

FIG. 3 is a simplified schematic view of an of an exemplary method for developing a field of producer wells to provide for the extraction of hydrocarbon fluids from one or more corresponding subsurface reservoirs in accordance with the present techniques;

FIG. 4 is a graph illustrating the manner in which cross-well strain data obtained from an offset well including one or more optical fibers may be used to detect fracture conductivity and/or proppant arrival corresponding to a producer well;

FIG. 5 is a schematic view of an exemplary mapping of DCNN-based features in accordance with the present techniques, specifically, a mapping of the first principal component (PC1) versus the second principal component (PC2);

FIG. 6 is a graph of a receiver operating characteristic (ROC) curve for an exemplary embodiment of the trained hybrid machine learning model in accordance with the present techniques;

FIG. 7 is a schematic view of an exemplary method for hydraulic fracture conductivity evaluation in accordance with the present techniques;

FIG. 8 is a block diagram of an exemplary cluster computing system that may be utilized to implement at least a portion of the present techniques; and

FIG. 9 is a block diagram of an exemplary non-transitory, computer-readable storage medium that may be used for the storage of data and modules of program instructions for implementing at least a portion of the present techniques.

It should be noted that the figures are merely examples of the present techniques and are not intended to impose limitations on the scope of the present techniques. Further, the figures are generally not drawn to scale, but are drafted for purposes of convenience and clarity in illustrating various aspects of the techniques.

DETAILED DESCRIPTION OF THE INVENTION

In the following detailed description section, the specific examples of the present techniques are described in connection with preferred embodiments. However, to the extent that the following description is specific to a particular embodiment or a particular use of the present techniques, this is intended to be for exemplary purposes only and simply provides a description of the embodiments. Accordingly, the techniques are not limited to the specific embodiments described below, but rather, include all alternatives, modifications, and equivalents falling within the true spirit and scope of the appended claims.

At the outset, and for case of reference, certain terms used in this application and their meanings as used in this context are set forth. To the extent a term used herein is not defined below, it should be given the broadest definition those skilled in the art have given that term as reflected in at least one printed publication or issued patent. Further, the present techniques are not limited by the usage of the terms shown below, as all equivalents, synonyms, new developments, and terms or techniques that serve the same or a similar purpose are considered to be within the scope of the present claims.

As used herein, the singular forms “a,” “an,” and “the” mean one or more when applied to any embodiment described herein. The use of “a,” “an,” and/or “the” does not limit the meaning to a single feature unless such a limit is specifically stated.

The term “and/or” placed between a first entity and a second entity means one of (1) the first entity, (2) the second entity, and (3) the first entity and the second entity. Multiple entities listed with “and/or” should be construed in the same manner, i.e., “one or more” of the entities so conjoined. Other entities may optionally be present other than the entities specifically identified by the “and/or” clause, whether related or unrelated to those entities specifically identified. Thus, as a non-limiting example, a reference to “A and/or B,” when used in conjunction with open-ended language such as “including,” may refer, in one embodiment, to A only (optionally including entities other than B); in another embodiment, to B only (optionally including entities other than A); in yet another embodiment, to both A and B (optionally including other entities). These entities may refer to elements, actions, structures, steps, operations, values, and the like.

As used herein, the term “any” means one, some, or all of a specified entity or group of entities, indiscriminately of the quantity.

The phrase “at least one,” when used in reference to a list of one or more entities (or elements), should be understood to mean at least one entity selected from any one or more of the entities in the list of entities, but not necessarily including at least one of each and every entity specifically listed within the list of entities, and not excluding any combinations of entities in the list of entities. This definition also allows that entities may optionally be present other than the entities specifically identified within the list of entities to which the phrase “at least one” refers, whether related or unrelated to those entities specifically identified. Thus, as a non-limiting example, “at least one of A and B” (or, equivalently, “at least one of A or B,” or, equivalently, “at least one of A and/or B”) may refer, in one embodiment, to at least one, optionally including more than one, A, with no B present (and optionally including entities other than B); in another embodiment, to at least one, optionally including more than one, B, with no A present (and optionally including entities other than A); in yet another embodiment, to at least one, optionally including more than one, A, and at least one, optionally including more than one, B (and optionally including other entities). In other words, the phrases “at least one,” “one or more,” and “and/or” are open-ended expressions that are both conjunctive and disjunctive in operation. For example, each of the expressions “at least one of A, B, and C,” “at least one of A, B, or C,” “one or more of A, B, and C,” “one or more of A, B, or C,” and “A, B, and/or C” may mean A alone, B alone, C alone, A and B together, A and C together, B and C together, A, B, and C together, and optionally any of the above in combination with at least one other entity.

As used herein, the phrase “based on” does not mean “based only on,” unless expressly specified otherwise. In other words, the phrase “based on” means “based only on,” “based at least on,” and/or “based at least in part on.”

As used herein, the terms “example,” exemplary,” and “embodiment,” when used with reference to one or more components, features, structures, or methods according to the present techniques, are intended to convey that the described component, feature, structure, or method is an illustrative, non-exclusive example of components, features, structures, or methods according to the present techniques. Thus, the described component, feature, structure, or method is not intended to be limiting, required, or exclusive/exhaustive; and other components, features, structures, or methods, including structurally and/or functionally similar and/or equivalent components, features, structures, or methods, are also within the scope of the present techniques.

As used herein, the term “field” (sometimes referred to as an “oil and gas field” or a “hydrocarbon field”) refers to an area for which hydrocarbon production operations are to be performed to provide for the extraction of hydrocarbon fluids from one or more corresponding subterranean formation.

The term “fracture” refers to a crack or surface of breakage induced by an applied pressure or stress within a subterranean formation.

As used herein, the term “fracture conductivity” or “hydraulic fracture conductivity” refers to the ability of a fluid to flow through a fracture at various stress (or pressure) levels, which is based, at least in part, on the permeability and thickness of the fracture.

The term “hydraulic fracturing” refers to a process for creating fractures that extend from a wellbore into a reservoir, so as to stimulate the flow of hydrocarbon fluids from the reservoir into the wellbore. A fracturing fluid is generally injected into the reservoir with sufficient pressure to create and extend multiple fractures within the reservoir, and a proppant material is used to “prop” or hold open the fractures after the hydraulic pressure used to generate the fractures has been released.

As used herein, the term “proppant” refers to particles that are mixed with fracturing fluid to hold open fractures that are formed within a near-wellbore region of a reservoir using a hydraulic fracturing process. The size, shape, strength, and density of the proppant material have a significant impact on the hydraulic fracturing process. Currently, commercial proppant materials include natural proppants, such as natural sands, resin-coated natural sands, shell fragments, and the like, and artificial proppants, such as sintered bauxite and ceramics, resin-coated or metal-coated ceramics, carbon-based proppants, lightweight proppants, ultra-lightweight proppants, and the like.

The term “substantially,” when used in reference to a quantity or amount of a material, or a specific characteristic thereof, refers to an amount that is sufficient to provide an effect that the material or characteristic was intended to provide. The exact degree of deviation allowable may depend, in some cases, on the specific context.

As used herein, the term “surface” refers to the uppermost land surface of a land well, or the mud line of an offshore well, while the term “subsurface” (or “subterranean”) generally refers to a geologic strata occurring below the earth's surface. Moreover, as used herein, “surface” and “subsurface” are relative terms. The fact that a particular piece of equipment is described as being on the surface does not necessarily mean it must be physically above the surface of the earth but, rather, describes only the relative placement of the surface and subsurface pieces of equipment. In that sense, the term “surface” may generally refer to any equipment that is located above the casing strings and other equipment that is located inside the wellbore. Moreover, according to embodiments described herein, the terms “downhole” and “subsurface” are sometimes used interchangeably, although the term “downhole” is generally used to refer specifically to the inside of the wellbore.

The term “wellbore” refers to a borehole drilled into a subterranean formation. The borehole may include vertical, deviated, highly deviated, and/or horizontal sections. The term “wellbore” also includes the downhole equipment associated with the borehole, such as the casing strings, production tubing, gas lift valves, and other subsurface equipment. Relatedly, the term “hydrocarbon well” (or simply “well”) includes the wellbore in addition to the wellhead and other associated surface equipment.

Turning now to details of the present techniques, as described above, information regarding the manner in which proppant transports through fractures, particularly to far field, can be used for well planning purposes, such as by enabling the estimation of optimal well spacing and, potentially, reducing the total number of wells drilled for the field. This, in turn, increases the efficiency of the overall hydrocarbon production operation. However, according to current techniques, there is very limited understanding regarding how proppant transports through fractures. Accordingly, the present techniques alleviate this difficulty and provide related advantages as well. In particular, the present techniques provide hybrid machine learning modeling methods and systems for evaluating and comparing hydraulic fracture conductivity with respect to one or more producer wells using fiber optic strain data collected from one or more offset wells. More specifically, the present techniques combine features from a deep convolutional neural network (DCNN), physics-based features (including features obtained from the strain data, as described further herein), and statistics-based features. The combination of such features is then used to produce a hybrid machine learning model that can be used to evaluate and compare hydraulic fracture conductivity, as well as to predict the arrival of proppant at the offset well(s) in real-time.

According to the present techniques, one or more optical fibers are deployed within one or more offset wells (e.g., one or more offset producer wells and/or one or more dedicated monitor wells) to collect physical measurements of optical phase shift caused by hydraulic fracturing operations in one or more producer wells. The optical phase shift measurements are then converted to dynamic strain measurements, and a two-dimensional (2D) strain map is generated. A deep-learning-based feature extraction technique is then used to identify key features from the 2D strain map, including features relating to strain evolution with time at every point along the fiber optic cable(s). In addition, several additional physics-based features (including, for example, strain rate frequency and average strain magnitude) are calculated from the 2D strain map. These features are then used, in combination with DCNN-based features and statistics-based features, to generate a hybrid machine learning model that can be used to evaluate and compares fracture conductivities, as well as to predict the arrival of proppant at the offset well(s) in real-time. A metric that combines the number of observed conductive fractures may then be used to determine an optimal well spacing plan for the field, and producer wells may then be drilled according to the well spacing plan.

Turning now to a detailed description of the figures, FIGS. 1 and 2 provide examples of wells that may be utilized to perform the techniques described herein. Within such figures, elements that serve a similar (or at least substantially similar) purpose may be labeled with like numbers. Moreover, in general, elements that are likely to be included in a particular embodiment are illustrated in solid lines, while elements that may be optional (depending, in part, on the particular type of well and/or the details of the particular embodiment) are illustrated in dashed lines. However, elements that are shown in solid lines may not be essential to all embodiments and, in some embodiments, may be omitted without departing from the scope of the present techniques. Generally speaking, those skilled in the art will appreciate that the schematic views of FIGS. 1 and 2 are not intended to indicate that the well(s) described herein are to include all of the components shown in the figures in every embodiment, or that the well(s) are limited to only such components. Rather, any number of components may be added to, or omitted from, the well(s) without departing from the scope of the present techniques.

FIG. 1 is a schematic view of an exemplary well 100 that may be utilized in accordance with the present techniques, while FIG. 2 is a simplified schematic view of multiple wells 100 that may be utilized in accordance with the present techniques, including a producer well 100A and an offset well 100B. More specifically, FIG. 1 is a more detailed illustration of examples of components/structures that may be included in wells according to the present techniques. In some embodiments, the well 100 of FIG. 1 is a producer well for which the present techniques are performed to make determinations regarding fracture conductivity within the hydraulic fractures corresponding to the well. In other embodiments, the well 100 of FIG. 1 is an offset well that is used to collect data relating to physics-based features for the present techniques. In such embodiments, the offset well may be either a separate producer well, a dedicated monitor well, or any other suitable type of well that is offset from the producer well, depending on the details of the particular implementation. Moreover, FIG. 2 is an illustration of an exemplary orientation and/or configuration of two wells 100, including the producer well(s) and the offset well(s) that are utilized according to embodiments described herein. With this in mind, any of the structures, components, functions, and/or features that are illustrated herein with reference to the well 100 of FIG. 1 may be included within either the producer well 100A or the offset well 100B (or, in some cases, both wells 100A and 100B) of FIG. 2, depending on the details of the particular implementation.

As shown in FIG. 1, the well 100 includes a wellbore 102 that extends between a surface region 104 and a subsurface region 106. In various embodiments, the subsurface region 106 includes a subterranean formation (or reservoir) from which hydrocarbon fluids are to be extracted and produced using the well 100 (and/or one or more other wells within the field).

In various embodiments, the well 100 includes a number of structures/components that enable the collection of data relating to physics-based features of the well 100 (and/or one or more other wells within the field). In various embodiments, such structures/components include one or more optical fibers 108, which extend and/or are positioned within the wellbore 102. Moreover, in some embodiments, such structures/components also include a spectral gamma logging tool 110 and/or a series of distributed pressure gauges 112, both of which extend and/or are positioned within the wellbore 102.

In various embodiments, the well 100 includes a computing system 114 that is configured to direct and control the execution of at least a portion of the present techniques. More specifically, the computing system 114 is configured to execute (either alone or with the aid of one or more remote computing systems, including, for example, one or more computing systems corresponding to one or more other wells within the field) a hybrid machine learning modeling process for hydraulic fracture conductivity evaluation. To that end, the computing system 114 may include any suitable component(s), structure(s), and/or device(s) that are adapted, configured, designed, constructed, and/or programmed to perform the techniques described herein. As examples, the computing system 114 may include an electronic controller, dedicated controller, special-purpose controller, personal computer, special-purpose computer, or the like. In various embodiments, the computing system 114 includes one or more processors and one or more non-transitory, computer-readable storage media 116 that include, define, and/or store computer-executable instructions, programs, and/or code, where such computer-executable instructions direct the processor(s) to perform any suitable portion, or subset, of the present techniques, as described further herein. Moreover, the computing system 114 may also include any number of additional components, including (but not limited to) one or more display devices, one or more memory devices, one or more communication connection devices, and the like.

Additionally or alternatively, the computing system 114 may include one or more separate computing systems, optionally corresponding to multiple wells in the field. In such embodiments, the computing system 114 may be communicably coupled to such remote computing system(s), with at least a portion of the computer-executable instructions corresponding to the present techniques being stored and/or executed by the remote computing system(s). In some embodiments, a single computing system (e.g., either the computing system 114 or another remote computing system) acts as the main computing system for executing the present techniques, with other computing system(s) cooperating to provide data and/or execute various functions throughout the process.

In various embodiments, the computing system 114 includes (and/or is communicably coupled to) an optical fiber controller 118 that permits and/or facilitates the initiation, regulation, and/or control of the measurement of strain data with the optical fiber(s) 108. In such embodiments, the optical fiber controller 118 may include an optical signal generator 120, optical signal receiver 122, and/or optical signal analyzer 124. In some embodiments, the optical fiber controller 118 and the optical fiber(s) 108 together may be referred to as a “distributed acoustic sensing (DAS) system.”

The optical signal generator 120 may be configured to generate optical signals and/or to provide the optical signals to initiation location(s) 126, such as uphole end(s), of the optical fiber(s) 108. The optical signals may then be conveyed away from the initiation location(s) 126, in a downhole direction 128, and/or along the length(s) of the optical fiber(s) 108 and may be scattered at a number of distributed sensing locations 130 that are spaced apart along the length(s) of the optical fiber(s) 108. Respective scattered fractions of the optical signals, which are scattered at each distributed sensing location 130, may then be conveyed along the length(s) of the optical fiber(s) 108, in an uphole direction 132, and/or toward the initiation location(s) 126 and may be detected, with the optical signal receiver 122, at detection location(s) 134 of the optical fiber(s) 108. The optical signal receiver 122 may then convey data regarding the respective scattered fractions of the optical signals to the optical signal analyzer 124, which may analyze and/or quantify the respective scattered fractions of the optical signals.

The above-described process may be repeated a number of times, or even continuously, as hydraulic fractures, such as exemplary hydraulic fracture 136, are propped with proppant 138 during the hydraulic fracturing operation. For example, in various embodiments, pressure signals induced in a producer well, such as via the pumping down of plugs at a slow rate, introduces pressure signals that cause deformation of the optical fiber(s) 108, which may cause strain within the optical fiber(s) 108. This strain within the optical fiber(s) 108 may be measured, detected, and/or quantified via changes in the respective scattered fractions of the optical signals that are scattered at each distributed sensing location 130, thereby permitting and/or facilitating the generation of data regarding strain in the optical fiber(s) 108, both as a function of position along the length(s) of the optical fiber(s) 108 and as a function of time during the progression of the hydraulic fracturing operation. In this manner, the optical fiber(s) 108, in combination with the optical fiber controller 118, provide for the collection of strain data that are used to determine physics-based features to be used as input for the hybrid machine learning model training process described herein.

In some embodiments, the computing system 114 also includes (and/or is communicably coupled to) a spectral gamma ray logging tool controller 140 that is configured to direct, facilitate, and/or control the operation of the spectral gamma ray logging tool 110 that is deployed within the wellbore 102. In such embodiments, hydraulic fractures, such as the exemplary hydraulic fracture 136, include radioactive proppant tracers 142 that are deployed along with the proppant 138 and thereby become scattered throughout the respective fractures. Moreover, the spectral gamma ray logging tool 110, in combination with (or under the direction of) the spectral gamma ray logging tool controller 140, may be configured to detect the presence of such radioactive proppant tracers 142 by detecting gamma radiation emitted by such radioactive proppant tracers 142 and then converting the corresponding gamma rays to electronic pulses that can be measured, counted, and/or analyzed to determine the locations of the radioactive proppant tracers 142 within the fractures, including the hydraulic fracture 136. In this manner, the spectral gamma ray logging tool 110, in combination with the spectral gamma ray logging tool controller 140, may provide for the collection of radioactive proppant tracer data that may be used to determine physics-based features to be used as additional input for the hybrid machine learning model training process described herein.

In some embodiments, the computing system 114 also includes (and/or is communicably coupled to) a distributed pressure gauge controller 144 that is configured to direct, facilitate, and/or control the operation of the distributed pressure gauges 112 that are deployed within the wellbore 102. In particular, the distributed pressure gauges 112, in combination with (or under the direction of) the distributed pressure gauge controller 144, may be configured to measures depletion as a function of distance from a producer well, where the amount of depletion in a particular region may indicate the extent to which hydraulic fractures in such region are propped with proppant. In this manner, distributed pressure gauges 112, in combination with the distributed pressure gauge controller 144, may provide for the collection of pressure depletion data that may be used to determine physics-based features to be used as additional input for the hybrid machine learning model training process described herein.

The correlation between the data obtained using the optical fiber(s) 108, the spectral gamma ray logging tool 110, and the distributed pressure gauges 112, as well as the manner in which such data correspond to the fracture conductivity within the corresponding hydraulic fractures, are shown below in Table 1.

TABLE 1
Labels	Indicator
More Conductive	Fracture hits close to distributed pressure gauges
	that showed depletion
	Fracture hits that showed strain signals during
	plug pump-down
	Fracture hits close to locations where radioactive
	proppant tracers were observed
Likely Non-	Fracture hits that do not show strain signals
Conductive	during plug pump-down
Non-Conductive	Fracture hits that occur very late during plug
	pump-down
	Fracture hits at large distances

Therefore, as shown in Table 1, a large amount of information regarding hydraulic fracture conductivity for a producer well may be obtained using optical fibers, spectral gamma ray logging tools, and/or distributed pressure gauges deployed within one or more offset wells.

As shown in FIG. 1, the well 100 may also include a downhole tubular 146, such as a casing string. The downhole tubular 146, when present, may extend within the wellbore 102 and may define, or at least partially bound, a tubular conduit 148. In such a configuration, the wellbore 102 and the downhole tubular 146 together may define, or at least partially bound, an annular space 150. Also in such a configuration, the optical fiber(s) 108, the spectra gamma ray logging tool 110, and/or the distributed pressure gauges 112 may extend within the tubular conduit 146 and/or within the annular space 150, as illustrated.

In some embodiments, the optical fiber(s) 108 and/or the distributed pressure gauges 112 may be rigidly and/or operatively attached to the wellbore 102 and/or to the downhole tubular 146. As an example, cement 152 may be positioned within the annular space 150, and the optical fiber(s) 108 and/or the distributed pressure gauges 112 may extend within the cement 152. As another example, the optical fiber(s) 108 and/or the distributed pressure gauges 112 may be attached or otherwise secured, tethered, or coupled to an internal and/or external surface of the downhole tubular 146 at a number of locations. Moreover, in some embodiments, the optical fiber(s) 108 and/or the distributed pressure gauges 112 are permanently installed and/or positioned within the wellbore 102. In other embodiments, the optical fiber(s) 108 and/or the distributed pressure gauges 112, along with the spectral gamma ray logging tool 110, may form a portion of one or more downhole assemblies, which may be temporarily and/or selectively positioned within the tubular conduit 148.

It should be noted that, according to embodiments described herein, the specific structures/components included within the well 100 may vary depending on whether the well is a producer well for which the hydraulic fracturing operation is being monitored or an offset well (e.g., another producer well or a dedicated monitor well) that is being used to monitor such hydraulic fracturing operation. This is explained in more detail with respect to FIG. 2. Specifically, FIG. 2 shows an exemplary producer well 100A and an exemplary offset well 100B. According to the embodiment shown in FIG. 2, each well 100A and 100B includes both horizontal and vertical well regions that are substantially parallel to one another. However, those skilled in the art will appreciate that the specific orientations, locations, and/or configurations of the wells 100A and 100B may vary widely, depending on the details of the specific implementation.

As shown in FIG. 2, hydraulic fractures, such as the exemplary hydraulic fracture 136, extend from the producer well 100A, which may be undergoing a hydraulic fracturing operation that is being monitored in real-time according to the present techniques. In such embodiments, the hydraulic fractures, including the exemplary hydraulic fracture 136, are propped with the proppant 138 and, optionally, may include the radioactive proppant tracers 142 that are deposited within the fractures along with the proppant.

As indicated in FIG. 2, the offset well 100B may include the primary structure/components for generating and collecting data relating to the hydraulic fracturing operation that is being implemented with respect to the producer well 100A. In particular, the offset well 100B may include the structure/components for generating data relating to the physics-based features that are used for the hybrid machine learning model training process described herein. Such structure/components include the optical fiber(s) 108 for collecting the stain data. In some embodiments, such structure/components also include the spectral gamma ray logging tool 110 for generating the radioactive proppant tracer data and/or the distributed pressure gauges 112 for generating the pressure depletion data, as described with respect to FIG. 1.

In some embodiments, and as illustrated in FIG. 2, at least a portion of the offset well 100B may extend within and/or through one or more hydraulic fractures, e.g., the hydraulic fracture 136, corresponding to the producer well 100A. In other embodiments, the offset well 100B may be spaced apart and/or distinct from the hydraulic fractures corresponding to the producer well 100A. Moreover, those skilled in the art will appreciate that the fracture-related data obtained according to the present techniques may be interpreted differently depending upon the relative orientation and/or distance between the producer well 100A and the offset well 100B.

FIG. 3 is a simplified schematic view of an of an exemplary method 300 for developing a field of producer wells to provide for the extraction of hydrocarbon fluids from one or more corresponding subsurface reservoirs in accordance with the present techniques. In various embodiments, the method 300 is executed using at least one producer well and at least one corresponding offset well within a particular field, in combination with one or more computing systems that are communicably coupled to the wells, as described with respect to FIGS. 1 and 2. As shown in FIG. 3, the method 300 may begin by executing hydraulic fracturing operation(s) for one or more producer wells within the field at block 302. At block 304, fracture-related data corresponding to the hydraulic fracturing operation(s) are generated using one or more corresponding offset wells within the field. As described with respect to FIGS. 1 and 2, such fracture-related data include strain data generated using one or more optical fibers (and corresponding optical fiber controller(s)) deployed within one or more offset wells. In various embodiments, such strain data are generated and collected simultaneously with the performance of particular stages of the hydraulic fracturing operation, in particular, during the pumping down of frac plugs and/or the positioning of perforations guns within the producer well(s). In some embodiments, the fracture-related data generated at block 304 also include radioactive proppant tracer data generated using one or more spectral gamma ray logging tools and/or pressure depletion data generated using distributed pressure gauges. Moreover, those skilled in the art will appreciate that other wellbore monitoring tools or components may also be used to generate additional fracture-related data according to embodiments described herein.

At block 306, deep-learning-based feature extraction techniques are performed to calculate, generate, or extract physics-based features from the fracture-related data of bock 304, and such physics-based features are then provided as input for training a hybrid machine learning model for hydraulic fracture conductivity evaluation (and proppant arrival estimation) at block 308. In particular, the strain data and, optionally, the radioactive proppant tracer data and/or pressure depletion data are used to extract the physics-based features. Turning specifically to the strain data generated using the optical fiber(s), in various embodiments, such strain data are used to generate a 2D strain map for each hydraulic fracturing event. Physics-based features are then calculated, generated, or extracted from the 2D strain map at block 306. Such physics-based features may include (but are not limited to): (a) post arrival average rate magnitude, which is the average magnitude of strain rate after fracture arrival and can be used to determine the decay of the fracture opening; (b) log low rate count, which is the log of the number of strain rate points with less than 5% of the maximum and can be used to determine the dynamics of the strain signals; (c) average strain magnitude, which is the average magnitude of the strain; (d) fracture time ratio, which is the time from fracture arrival to pump off over time from pump on to pump off and can be used to determine fracture arrival time; (e) post arrival average rate frequency, which is the average frequency of the strain rate after fracture arrival; and/or (f) zero crossing frequency, which is the frequency at which the signal crosses zero and can be used to determine the dynamics of the strain signals. Additional examples of such physics-based features include: (g) maximum strain magnitude; (h) average strain magnitude after fracture opening; (i) average tail frequency after fracture opening; (j) logarithm of frequency defined by Fourier transform; (k) fracture time; (l) Otsu threshold; (m) positive/negative strain count ratio; (n) brightness; (o) timestamp count of positive strain rate; (p) timestamp count of negative strain rate; and the like.

Notably, the present techniques are based, at least in part, on the calculation, generation, or extraction of the aforementioned physics-based features, which enable the detection or determination of fracture conductivity and/or proppant arrival based on cross-well strain data (where the term “cross-well” refers to the fact that the strain data may be obtained from one or more offset wells, rather than directly from the producer well undergoing hydraulic fracturing). This is illustrated by FIG. 4, which is a graph 400 illustrating the manner in which cross-well strain data obtained from an offset well 402 including one or more optical fibers may be used to detect fracture conductivity and/or proppant arrival corresponding to a producer well 404. According to embodiments described herein, both one-dimensional and two-dimensional strain rate histories are used, at least in part, to identify fracture hits and to correlate such fracture hits with available labels to evaluate the relative conductivity between fractures. Moreover, as described herein, such strain rate histories are obtained using optical fibers, which are configured to sense the stress and strain fields around such fractures. Such stress and strain fields can be used as a proxy for fracture width at the monitoring location (i.e., the location of the optical fiber) and, hence, may be analyzed to determine information regarding proppant arrival within the fractures at such locations.

In various embodiments, DCNN-based features are generated or extracted at block 310 and are also input to the hybrid machine learning model training process of block 308. Such DCNN-based features may include (but are not limited to) the first and second principal components of GAF-DCNN features, which may be abbreviated as “PC1” and “PC2,” respectively, and relate to the temporal correlation between time series. Moreover, in various embodiments, such DCNN-based features are generated or extracted from the strain data as well as, optionally, the radioactive proppant tracer data and/or pressure depletion data described herein. For example, in various embodiments, DCNN-based features are generated or extracted from the 2D strain map using a deep-learning-based feature extraction technique. Specifically, according to such deep-learning-based feature extraction technique, the 2D strain map for each hydraulic fracturing event may be converted to a strain rate map, which may then be averaged to a time series of averaged strain rate over all depths that are considered for the hydraulic fracturing event. A Gramian Angular Field (GAF) map is then calculated for each times series, and the GAF map is loaded into a deep convolutional neural network (DCNN), such as a VGG-16 DCNN. Moreover, in various embodiments, the GAF map encodes the time series and its autocorrelation into an image, which may improve the classification accuracy for the model training process. In various embodiments, the DCNN (e.g., a VGG-16 DCNN) is pretrained using an open image-based training dataset, such as images from ImageNet, and the top layers of the DCNN are then removed such that the output is an array of features. The features may then be mapped to the principal components (e.g., PC1 and PC2) using principal component analysis techniques, and such principal components may be input as at least a portion of the DCNN-based features for the modeling training process of block 308.

FIG. 5 is a schematic view of an exemplary mapping 500 of DCNN-based features in accordance with the present techniques, specifically, a mapping of the first principal component (PC1) versus the second principal component (PC2). As shown in FIG. 5, conductive samples are marked by filled-in circles, while nonconductive samples are marked by unfilled-in circles. In various embodiments, both PC1 and PC2 are input as features for the hybrid machine learning model training process of block 308.

Furthermore, in various embodiments, statistics-based features are calculated, generated, or extracted at block 312 and are input to the hybrid machine learning model training process of block 308. Such statistics-based features may include (but are not limited to) a positive/negative count ratio, which is the ratio between the area of positive pixels and the area of negative pixels and can be used to determine the ratio between total extension and total compression, and the negative time count, which is the number of strain rate points below zero and can be used to determine the portion of signals that are compression signals. In various embodiments, at least a portion of such statistics-based features may be calculated, generated, or extracted, at least in part, from the strain data as well as, optionally, the radioactive proppant tracer data and/or pressure depletion data described herein.

Turning now specifically to the hybrid machine learning model training process of block 308, the model may be trained using the DCNN-based features, the physics-based features, and the statistics-based features. Specifically, such features may be used to train the hybrid machine learning model according to a transfer learning process in which the DCNN that is pretrained with the images from the open image-based training dataset is used, in combination with the features described above, to train the hybrid machine learning model. Specifically, in various embodiments, all the features are first ranked based on an importance score, such as a permutation importance score, for example. The top “n” features are then used to generate the hybrid machine learning model for evaluating hydraulic fracture conductivity and estimating proppant arrival. In some specific embodiments, the hybrid machine learning model training technique includes an extreme gradient boosting (XGB) technique, and the generated model is an XGB model, although those skilled in the art will appreciate that any other suitable hybrid model training technique may alternatively be utilized. Moreover, those skilled in the art will appreciate that the number “n” of features to be used for the model training process may vary depending on the details of the particular implementation. In some embodiments, “n” is equal to 10, meaning that the ten features with the highest importance scores are selected for training the model.

At block 314, the generated hybrid machine learning model is applied to the field in question to generate an optimal (or substantially optimal) well spacing plan for the field. In particular, applying the hybrid machine learning model to the field provides data regarding the manner in which hydraulic fractures are growing (or tend to grow) in the particular field (including the times, locations, and/or extent of proppant arrival during the slurry stage of the hydraulic fracturing operation), thus enabling the generation of a development strategy in which the wells are optimally (or substantially optimally) spaced, located, oriented, and/or configured to provide for maximum hydrocarbon extraction from the corresponding subsurface reservoir(s). In this manner, the generated well spacing plan may improve the overall efficiency of the corresponding hydrocarbon production operation by reducing the total number of wells that are to be drilled for the field and/or by improving the spacing, locations, orientations, and/or configurations of such wells, particularly with respect to each other.

At optional block 316, the field is developed according to the well spacing plan. This may include drilling and/or completing wells (and/or causing wells to be drilled and/or completed) in accordance with the well spacing plan. In this manner, the present techniques provide a practical application in the field of hydrocarbon production by utilizing domain-specific, fracture-related data from the particular field to generate the well spacing plan and then actually implementing such well spacing plan to drill and/or complete a number of wells, thus facilitating the physical extraction of hydrocarbon fluids from a hydrocarbon reservoir corresponding to the field.

Those skilled in the art will appreciate that the exemplary method 300 of FIG. 3 is susceptible to modification without altering the technical effect provided by the present techniques. In practice, the exact manner in which the method 300 is implemented will depend, at least in part, on the details of the specific implementation. For example, in some embodiments, some of the blocks shown in FIG. 3 may be altered or omitted from the method 300 and/or new blocks may be added to the method 300.

In various embodiments, the hybrid machine learning model training process described herein outputs a hybrid machine learning model (e.g., an XGB model) with a high degree of performance and accuracy. This is illustrated by FIG. 6, which is a graph 600 of a receiver operating characteristic (ROC) curve for an exemplary embodiment of the trained hybrid machine learning model in accordance with the present techniques. As shown in FIG. 6, the exemplary trained model has excellent performance, with an accuracy of 0.9 and an area under the ROC (AUROC) of 0.95 for the validation dataset.

FIG. 7 is a schematic view of an exemplary method 700 for hydraulic fracture conductivity evaluation in accordance with the present techniques. The method 700 is executed by one or more computing systems including one or more processors, such as the computing system 114 described with respect to FIG. 1 and/or the cluster computing system 800 described with respect to FIG. 8, or any suitable variation(s) thereof.

The method 700 begins at block 702 with the measurement of fracture-related data corresponding to a hydraulic fracturing operation performed with respect to one or more producer wells in a field, where the fracture-related data include strain data measured using one or more optical fibers deployed within one or more offset wells in the field. In some embodiments, the fracture-related data also include radioactive proppant tracer data measured using one or more spectral gamma ray logging tools deployed within the offset well(s) in the field. Additionally or alternatively, in some embodiments, the fracture-related data also include pressure depletion data measured using distributed pressure gauges deployed within the offset well(s) in the field.

At block 704, DCNN-based features, physics-based features, and statistics-based features are extracted using the fracture-related data. In various embodiments, extracting the DCNN-based features using the fracture-related data includes performing deep-learning-based feature extraction by: generating 2D strain maps from the strain data; converting each 2D strain map to a strain rate map; averaging each strain rate map to a time series of averaged strain rate; calculating a GAF map for each time series; loading each GAF map into a pretrained DCNN; removing top layers of the DCNN to generate an array of features; mapping the array of features to two or more principal components; and outputting the two or more principal components as at least a portion of the DCNN-based features. Moreover, in various embodiments, the method 700 includes pretraining the DCNN using an open image-based training dataset. Furthermore, in various embodiments, extracting the physics-based features using the fracture-related data includes generating the 2D strain maps from the strain data and calculating at least a portion of the physics-based features from the 2D strain maps.

The method 700 then proceeds to block 706 with the training of a hybrid machine learning model for evaluating hydraulic fracture conductivity corresponding to the hydraulic fracturing operation, where the training is performed using the DCNN-based features, the physics-based features, and the statistics-based features. In various embodiments, the method 700 includes training the hybrid machine learning model by performing transfer learning using the pretrained DCNN, in combination with the DCNN-based features, the physics-based features, and the statistics-based features. Moreover, in various embodiments, training the hybrid machine learning model includes ranking each of the DCNN-based features, the physics-based features, and the statistics-based features based on an importance score and then utilizing a specified number (e.g., “n”=10) of the features with the highest importance scores to train the hybrid machine learning model. Furthermore, in some embodiments, the method 700 includes training the hybrid machine learning model by performing XGB techniques. In such embodiments, the resulting trained hybrid machine learning model is an XGB model.

At block 708, the trained hybrid machine learning model is applied to generate a well spacing plan for the field. In some embodiments, applying the trained hybrid machine learning model to generate the well spacing plan for the field includes (but is not limited to) utilizing the trained hybrid machine learning model to calculate fracture conductivity and/or proppant arrival for the producer well(s) and generating the well spacing plan based on the calculated fracture conductivity and/or proppant arrival.

At optional block 710, the processor(s) implementing the method 700 then cause the generated well spacing plan to be applied to the field. In some embodiments, causing the well spacing plan to be applied to the field includes causing the one or more existing producer wells to be completed in the field according to the well spacing plan and/or causing one or more additional producer wells to be drilled and/or completed in the field according to the well spacing plan.

Those skilled in the art will appreciate that the exemplary method 700 of FIG. 7 is susceptible to modification without altering the technical effect provided by the present techniques. In practice, the exact manner in which the method is implemented will depend, at least in part, on the details of the specific implementation. For example, in some embodiments, some of the blocks shown in FIG. 7 may be altered or omitted from the method 700 and/or new blocks may be added to the method 700.

FIG. 8 is a block diagram of an exemplary cluster computing system 800 that may be utilized to implement at least a portion of the present techniques. The exemplary cluster computing system 800 shown in FIG. 8 has four computing units 802A, 802B, 802C, and 802D, each of which may perform calculations for a portion of the present techniques. However, one of ordinary skill in the art will recognize that the cluster computing system 800 is not limited to this configuration, as any number of computing configurations may be selected. For example, a smaller analysis may be run on a single computing unit, such as a workstation, while a large calculation may be run on a cluster computing system 800 having tens, hundreds, thousands, or even more computing units.

The cluster computing system 800 may be accessed from any number of client systems 804A and 804B over a network 806, for example, through a high-speed network interface 808. The computing units 802A to 802D may also function as client systems, providing both local computing support and access to the wider cluster computing system 800.

The network 806 may include a local area network (LAN), a wide area network (WAN), the Internet, or any combinations thereof. Each client system 804A and 804B may include one or more non-transitory, computer-readable storage media for storing the operating code and program instructions that are used to implement at least a portion of the present techniques, as described further with respect to the non-transitory, computer-readable storage media 116 and 900 of FIGS. 1 and 9, respectively. For example, each client system 804A and 804B may include a memory device 810A and 810B, which may include random access memory (RAM), read only memory (ROM), and the like. Each client system 804A and 804B may also include a storage device 812A and 812B, which may include any number of hard drives, optical drives, flash drives, or the like.

The high-speed network interface 808 may be coupled to one or more buses in the cluster computing system 800, such as a communications bus 814. The communication bus 814 may be used to communicate instructions and data from the high-speed network interface 808 to a cluster storage system 816 and to each of the computing units 802A to 802D in the cluster computing system 800. The communications bus 814 may also be used for communications among the computing units 802A to 802D and the cluster storage system 816. In addition to the communications bus 814, a high-speed bus 818 can be present to increase the communications rate between the computing units 802A to 802D and/or the cluster storage system 816.

In some embodiments, the one or more non-transitory, computer-readable storage media of the cluster storage system 816 include storage arrays 820A, 820B, 820C and 820D for the storage of models (including the hybrid machine learning model described herein), data (including the fracture-related data described herein, among other data used for implementing the present techniques), visual representations, results (such as graphs, charts, and the like used to convey results obtained using the present techniques), code, and other information concerning the implementation of at least a portion of the present techniques. The storage arrays 820A to 820D may include any combinations of hard drives, optical drives, flash drives, or the like.

Each computing unit 802A to 802D includes at least one processor 822A, 822B, 822C and 822D and associated local non-transitory, computer-readable storage media, such as a memory device 824A, 824B, 824C and 824D and a storage device 826A, 826B, 826C and 826D, for example. Each processor 822A to 822D may be a multiple core unit, such as a multiple core central processing unit (CPU) or a graphics processing unit (GPU). Each memory device 824A to 824D may include ROM and/or RAM used to store program instructions for directing the corresponding processor 822A to 822D to implement at least a portion of the present techniques. Each storage device 826A to 826D may include one or more hard drives, optical drives, flash drives, or the like. In addition, each storage device 826A to 826D may be used to provide storage for models, intermediate results, data, images, or code used to implement at least a portion of the present techniques.

The present techniques are not limited to the architecture or unit configuration illustrated in FIG. 8. For example, any suitable processor-based device may be utilized for implementing at least a portion of the embodiments described herein, including (without limitation) personal computers, laptop computers, computer workstations, mobile devices, and multi-processor servers or workstations with (or without) shared memory. Moreover, the embodiments described herein may be implemented, at least in part, on application specific integrated circuits (ASICs) or very-large-scale integrated (VLSI) circuits. In fact, those skilled in the art may utilize any number of suitable structures capable of executing logical operations according to the embodiments described herein.

FIG. 9 is a block diagram of an exemplary non-transitory, computer-readable storage medium 900 that may be used for the storage of data and modules of program instructions for implementing at least a portion of the present techniques. The non-transitory, computer-readable storage medium 900 may include a memory device, a hard disk, and/or any number of other devices, as described herein. A processor 902 may access the non-transitory, computer-readable storage medium 900 over a bus or network 904. While the non-transitory, computer-readable storage medium 900 may include any number of modules (and sub-modules) for implementing the present techniques, in some embodiments, the non-transitory, computer-readable storage medium 500 includes a data measurement module 906 for measuring fracture-related data corresponding to a hydraulic fracturing operation performed with respect to producer well(s) in a field; a feature extraction module 908 for extracting DCNN-based features, physics-based features, and statistics-based features using the fracture-related data; a model training module 910 for training a hybrid machine learning model for evaluating hydraulic fracture conductivity corresponding to the hydraulic fracturing operation; and a model application module 912 for applying the trained hybrid machine learning model to generate a well spacing plan for the field.

In one or more embodiments, the present techniques may be susceptible to various modifications and alternative forms, such as the following embodiments as noted in paragraphs 1 to 21.

Paragraph 1. A method for hydraulic fracturing conductivity evaluation with respect to a producer well, where the method is executed via a processor of a computing system, and where the method includes: measuring fracture-related data corresponding to a hydraulic fracturing operation performed with respect to least one producer well in a field, where the fracture-related data include strain data measured using at least one optical fiber deployed within at least one offset well in the field; extracting deep convolutional neural network (DCNN)-based features, physics-based features, and statistics-based features using the fracture-related data; training a hybrid machine learning model for evaluating hydraulic fracture conductivity corresponding to the hydraulic fracturing operation, where the training is performed using the DCNN-based features, the physics-based features, and the statistics-based features; and applying the trained hybrid machine learning model to generate a well spacing plan for the field.

Paragraph 2. The method of paragraph 1, where the fracture-related data further include radioactive proppant tracer data measured using at least one spectral gamma ray logging tool deployed within the at least one offset well in the field.

Paragraph 3. The method of paragraph 1 or 2, where the fracture-related data further include pressure depletion data measured using distributed pressure gauges deployed within the at least one offset well in the field.

Paragraph 4. The method of any of paragraphs 1 to 3, where extracting the DCNN-based features using the fracture-related data includes performing deep-learning-based feature extraction by: generating two-dimensional (2D) strain maps from the strain data; converting each 2D strain map to a strain rate map; averaging each strain rate map to a time series of averaged strain rate; calculating a Gramian Angular Field (GAF) map for each time series; loading each GAF map into a pretrained DCNN; removing top layers of the DCNN to generate an array of features; mapping the array of features to at least two principal components; and outputting the at least two principal components as at least a portion of the DCNN-based features.

Paragraph 5. The method of paragraph 4, including pretraining the DCNN using an open image-based training dataset.

Paragraph 6. The method of any of paragraphs 1 to 5, where extracting the physics-based features using the fracture-related data includes: generating 2D strain maps from the strain data; and calculating at least a portion of the physics-based features from the 2D strain maps.

Paragraph 7. The method of any of paragraphs 1 to 6, including training the hybrid machine learning model by performing transfer learning using a pretrained DCNN, in combination with the DCNN-based features, the physics-based features, and the statistics-based features.

Paragraph 8. The method of any of paragraphs 1 to 7, where training the hybrid machine learning model includes: ranking each of the DCNN-based features, the physics-based features, and the statistics-based features based on an importance score; and utilizing a specified number of features with highest importance scores to train the hybrid machine learning model.

Paragraph 9. The method of any of paragraphs 1 to 8, where training the hybrid machine learning model includes performing extreme gradient boosting (XGB), and where the trained hybrid machine learning model includes an XGB model.

Paragraph 10. The method of any of paragraphs 1 to 9, where applying the trained hybrid machine learning model to generate the well spacing plan for the field includes: utilizing the trained hybrid machine learning model to calculate at least one of fracture conductivity or proppant arrival for the at least one producer well; and generating the well spacing plan based on the at least one of the fracture conductivity or the proppant arrival.

Paragraph 11. The method of any of paragraphs 1 to 10, further including causing the generated well spacing plan to be applied to the field.

Paragraph 12. The method of paragraph 11, where causing the generated well spacing plan to be applied to the field includes at least one of: causing the at least one producer well to be completed in the field according to the well spacing plan; or causing at least one additional producer well to be drilled in the field according to the well spacing plan.

Paragraph 13. A method for developing a field of producer wells, including: executing a hydraulic fracturing operation for a producer well in a field; generating fracture-related data corresponding to the hydraulic fracturing operation for the producer well using an offset well, where the fracture-related data include strain data measured using an optical fiber deployed within the offset well; extracting DCNN-based features, physics-based features, and statistics-based features using the fracture-related data; training a hybrid machine learning model for evaluating hydraulic fracture conductivity corresponding to the hydraulic fracturing operation, where the training is performed using the DCNN-based features, the physics-based features, and the statistics-based features; applying the trained hybrid machine learning model to generate a well spacing plan for the field; and developing the field according to the generated well spacing plan.

Paragraph 14. The method of paragraph 13, where the fracture-related data further include radioactive proppant tracer data measured using at least one spectral gamma ray logging tool deployed within the at least one offset well in the field.

Paragraph 15. The method of paragraph 13 or 14, where the fracture-related data further include pressure depletion data measured using distributed pressure gauges deployed within the at least one offset well in the field.

Paragraph 16. The method of any of paragraphs 13 to 15, where extracting the DCNN-based features using the fracture-related data includes performing deep-learning-based feature extraction by: generating 2D strain maps from the strain data; converting each 2D strain map to a strain rate map; averaging each strain rate map to a time series of averaged strain rate; calculating a GAF map for each time series; loading each GAF map into a pretrained DCNN; removing top layers of the DCNN to generate an array of features; mapping the array of features to at least two principal components; and outputting the at least two principal components as at least a portion of the DCNN-based features.

Paragraph 17. The method of any of paragraphs 13 to 16, including training the hybrid machine learning model by performing transfer learning using a pretrained DCNN, in combination with the DCNN-based features, the physics-based features, and the statistics-based features.

Paragraph 18. The method of any of paragraphs 13 to 17, where training the hybrid machine learning model includes performing XGB, and where the trained hybrid machine learning model includes an XGB model.

Paragraph 19. A computing system, including: a processor; and a non-transitory, computer-readable storage medium, including code configured to direct the processor to: access fracture-related data corresponding to a hydraulic fracturing operation performed with respect to least one producer well in a field, where the fracture-related data include strain data measured using at least one optical fiber deployed within at least one offset well in the field; extract DCNN-based features using the fracture-related data by performing deep-learning-based feature extraction, where performing the deep-learning-based feature extraction includes: generating 2D strain maps from the strain data; converting each 2D strain map to a strain rate map; averaging each strain rate map to a time series of averaged strain rate; calculating a GAF map for each time series; loading each GAF map into a pretrained DCNN; removing top layers of the DCNN to generate an array of features; mapping the array of features to at least two principal components; and outputting the at least two principal components as at least a portion of the DCNN-based features; extract physics-based features using the fracture-related data by calculating at least a portion of the physics-based features from the 2D strain maps; extract statistics-based features using the fracture-related data; train a hybrid machine learning model for evaluating hydraulic fracture conductivity corresponding to the hydraulic fracturing operation, where the training is performed using the pretrained DCNN, in combination with the DCNN-based features, the physics-based features, and the statistics-based features; and apply the trained hybrid machine learning model to generate a well spacing plan for the field.

Paragraph 20. The computing system of paragraph 19, where the non-transitory, computer-readable storage medium further includes code configured to direct the processor to cause the well spacing plan to be applied to the field.

Paragraph 21. The computing system of paragraph 19 or 20, wherein the non-transitory, computer-readable storage medium further includes code configured to direct the processor to train the hybrid machine learning model by: ranking each of the DCNN-based features, the physics-based features, and the statistics-based features based on an importance score; and utilizing a specified number of the features with the highest importance scores to train the hybrid machine learning model.

While the embodiments described herein are well-calculated to achieve the advantages set forth, it will be appreciated that such embodiments are susceptible to modification, variation, and change without departing from the spirit thereof. In other words, the particular embodiments described herein are illustrative only, as the teachings of the present techniques may be modified and practiced in different but equivalent manners apparent to those skilled in the art having the benefit of the teachings herein. Moreover, the systems and methods illustratively disclosed herein may suitably be practiced in the absence of any element that is not specifically disclosed herein and/or any optional element disclosed herein. While compositions and methods are described in terms of “comprising” or “including” various components or steps, the compositions and methods can also “consist essentially of” or “consist of” the various components and steps. Indeed, the present techniques include all alternatives, modifications, and equivalents falling within the true spirit and scope of the appended claims.